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A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large…

Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…

We consider the problem of learning stabilizable systems governed by nonlinear state equation $h_{t+1}=\phi(h_t,u_t;\theta)+w_t$. Here $\theta$ is the unknown system dynamics, $h_t $ is the state, $u_t$ is the input and $w_t$ is the…

Online continual learning (OCL) methods adapt to changing environments without forgetting past knowledge. Similarly, online time series forecasting (OTSF) is a real-world problem where data evolve in time and success depends on both rapid…

Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered…

One crucial factor behind the success of deep learning lies in the implicit bias induced by noise inherent in gradient-based training algorithms. Motivated by empirical observations that training with noisy labels improves model…

Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…

Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…

We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…

Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…

Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…

Can stochastic gradient methods track a moving target? We study the problem of tracking multidimensional time-varying parameters under noisy observations and possible model misspecification. Gradient-based filters update the time-varying…

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…

Deep learning involves a difficult non-convex optimization problem, which is often solved by stochastic gradient (SG) methods. While SG is usually effective, it may not be robust in some situations. Recently, Newton methods have been…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

The learning rate schedule is one of the most impactful aspects of neural network optimization, yet most schedules either follow simple parametric functions or react only to short-term training signals. None of them are supported by a…

The time it takes for a classifier to make an accurate prediction can be crucial in many behaviour recognition problems. For example, an autonomous vehicle should detect hazardous pedestrian behaviour early enough for it to take appropriate…

Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…

Fine-tuning pretrained models has become a standard approach to adapting pretrained knowledge to improve the accuracy on new sparse, imbalance datasets. However, issues arise when optimization falls into a collapsed state, where the model…

Pre-training data detection for LLMs is essential for addressing copyright concerns and mitigating benchmark contamination. Existing methods mainly focus on the likelihood-based statistical features or heuristic signals before and after…